A line of Hungarian police blocking the entrance to Keleti Station while Syrian refugees camp out another night on September 2, 2015.

Lower ground of Keleti Station in Budapest, Hungary, filled with hundreds of refugees overnighting on September 2, 2015.

Local pizza place offers free power to refugees to charge their phones in Budapest, Hungary on September 2, 2015.

Lower ground of Keleti Station in Budapest, Hungary, filled with hundreds of refugees overnighting on September 2, 2015.

By Arwa Damon and Laura Smith-Spark

BICSKE, Hungary (CNN) - Trains carrying migrants trying to get from Hungary to Austria were stopped Thursday at a station just outside the Hungarian capital, Budapest, where police were gathered at the side of the track.

The trains abruptly stopped at Bicske and the migrants on board were refusing to get off the trains.

Tents and desks were set up near the station in what the migrants feared was set up to be a relocation camp.

The main train station in Hungary's capital, Budapest, reopened Thursday -- but there was no good news for the crowds of weary migrants and refugees who've been waiting for days to board trains onward to Western Europe.

The migrants are free to travel to migrant camps in Hungary but won't be able to board an international train service, he said.

Budapest's Keleti station has become a focal point of the crisis currently engulfing parts of Europe, as an unprecedented wave of people -- mostly refugees fleeing conflict in Syria, Iraq and Afghanistan -- seek to reach Northern and Western Europe.

Hungary, while part of the European Union, is not the migrants' end destination but rather a transit point on a long journey north from Greece to wealthier nations like Austria and Germany, where they hope to claim asylum.

But Hungarian authorities say that under EU legislation, they can't allow people to travel without the proper documentation -- a valid passport, a ticket and any necessary visas.

Hungarian railway operator MAV said Thursday it had decided not to run direct trains from Budapest toward Western Europe "for safety reasons." International tickets will be accepted on domestic trains, it said.

It's not clear if migrants who catch regional trains from Budapest will be able to travel on to other countries once they reach Hungary's borders.

A CNN team got on a train packed with Syrian refugees as it left Keleti station on Thursday -- its destination unknown.

There was wide unease among the families on board, including young children, but those who spoke to CNN said they just couldn't stay in Keleti station any longer.

Some had heard the train was headed for the Hungarian-Austrian border, while others feared it might stop instead at one of the migrant camps.

Few want to go to the migrant camps set up by authorities, fearing that once there they may not be able to continue on to other EU states.

On Thursday, Hungarian Prime Minister Viktor Orban is meeting with other members of the European Union to figure out how to cope with the emergency.

Prime minister: 'Don't criticize Hungary'

Speaking to reporters in Brussels, Belgium, alongside European Parliament President Martin Schulz, Orban said the situation was not of his country's making.

"The problem is not just a European problem; the problem is a German problem," he said.

Germany's government said last month it expected up to 800,000 asylum seekers to come this year -- four times more than in 2014. But, Orban said, German Chancellor Angela Merkel has said that they must be registered before leaving Hungary.

"All of them would like to go to Germany, our job is to only register them," Orban said.

Without strict border controls, EU migrant quotas are "an invitation" for migrants to come, he said. "Turkey is a safe country, why don't you stay there?" he said, adding that migrants who reach Serbia should also stay put.

Hungary's right-wing government has faced criticism for erecting a barbed-wire fence along its more than 100-mile border with Serbia in a bid to prevent migrants' crossing illegally as they make their way north.

But Orban said his country was just trying to enforce EU rules and that new measures would be in place shortly. "Don't criticize Hungary for what is being done. Let Hungary do the job as it is written in the European regulations," he said.

Schulz warned that the European Union must work together. "This is a crucial moment for the European Union," he said. "A deeper split of the union is a risk."

While European leaders struggle to come up with a coherent plan, the men, women and children caught up in the crisis continue to suffer.

On Wednesday, some refugees in Budapest held up scraps of paper: "Help Syrians," they read. "Babies are tired."

"We hope you will save us," a Syrian refugee named Houriye told CNN. "I beg you to save us."

Mahmoud, a chemical engineer, said he was a successful businessman until he lost it all to Syria's war. The face of his 4-year-old son is scratched from a fall at a border crossing.

"It's too tough for me to see my family like this," he said.

EU foreign policy chief urges 'united' action

On Wednesday, Italy, Germany and France sought a united response to the worsening situation.

Foreign ministers Paolo Gentiloni of Italy, Frank-Walter Steinmeier of Germany and Laurent Fabius of France presented the European Union with a joint document calling for a revision of asylum rules and a fairer distribution of refugees, according to the Italian Foreign Ministry.

The effort came as the photo of a toddler's lifeless body -- one of 12 people who drowned off Turkey and washed up on a beach -- seemed to symbolize the gravity of the crisis.

The European Union's foreign policy chief, Federica Mogherini, urged "united" action and said the issue would be part of the next EU foreign ministers' meeting on Friday and Saturday. The EU Commission was meeting to prepare new proposals.

EU Council President Donald Tusk warned of a divide between Eastern and Western European nations in the way they handle the situation.

"Some member states are thinking about containing the wave of migration, symbolized by the controversial Hungarian fence. Others expect greater solidarity in advocating ... a so-called obligatory basis for quotas," he said.

A common approach must be found, he said, while making sure "people in need of international protection receive it, preferably as close to their home country as possible."

Joyful refugees reach Germany

Another batch of refugees, meanwhile, arrives in Munich with almost every train that pulls into the station.

Tired, hungry, weak from the heat, they speak of harrowing journeys -- and the joy of finally making it to Germany.

"It was so hard for us. It took a very long time," said a woman from Afghanistan. "Especially in Hungary, it was very difficult to get through Hungary. We had almost no food and water."

Germany's government has been more accepting of asylum seekers than some, but political leaders there have had to contend with xenophobic protests.

German Chancellor Angela Merkel said Monday that her country must show "flexibility" when it comes to dealing with the crisis.

Meanwhile in France, migrants shut down the Eurostar cross-channel service between England and France overnight Tuesday to Wednesday as they poured onto the tracks near Calais, the French entry to the Channel Tunnel. Trains between London and Paris and London and Brussels were turned back.

Caught in the middle of the confusion are the desperate men and women, with children in tow, who have fled wars in Syria and Iraq to embark on fraught, sometimes deadly voyages by land or by sea.

Border controls reinstated

EU rules usually allow people with proper documentation to travel through much of the European Union without border checks -- but the current influx of migrants has led to extraordinary measures in some places.

Italian authorities on Wednesday said they were temporarily reinstating border controls at the Italian-Austrian line in the region of Alto Adige in northern Italy, after being requested to do so by Bavarian authorities in Germany who say they are "overwhelmed" by the influx of migrants, according to a statement released by Italy's Bolzano prefecture.

Bavaria has had a great number of refugees arriving mainly from the Balkan route and the situation is getting difficult to handle, the Italian statement said.

"Work is in process to find new shelters for the continuously growing number of refugees," it said.

Czech authorities, meanwhile, said they have started to remove migrants from trains.

Republican Sen. Marco Rubio is being challenged by angry students, teachers and parents who are demanding stronger gun-control measures after a shooting rampage claimed 17 lives at a Florida high school.

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